Cylindrical hobs are used for the manufacture of external cylindrical gears, cross helical gears and worm gears. The manufacture of internal gears is not possible using a cylindrical hobbing tool due to mutilation left and right to the center line. The profile of a cylindrical hob is a trapezoid which reflects the pressure angle and module (depth and spacing) of the part to be manufactured. This so-called reference profile can be observed in a plane through the center of the hob in an axial plane (e.g. a horizontal plane) as illustrated by FIG. 1. The directions of the hob axis, H, and the workpiece axis, W, in the case of spur gear manufacturing are perpendicular to one another or slightly inclined about an angle, which is the same or similar magnitude as the lead angle of the hob teeth.
FIG. 1 shows a three dimensional graphic of a cylindrical hob and virtual generating rack. The hob simulates the profile of the generating rack in a horizontal plane (the drawing shows the top profile plane of the rack), which in the simple case shown in FIG. 1 contains the axis of rotation of the hob. If the hob rotates (as indicated by “F”), the generating rack will move in direction “G”. In case of a hob with one start, one revolution will shift the rack one pitch in direction G. In order to cut a gear with the face width of the rack in FIG. 1, the hob has to move in direction “E”, until the horizontal plane (which includes the hob axis) reaches the bottom profile plane of the rack. Thus, the hob teeth show the rack profile on their front face, if the front face coincides with an axial plane. Each hob revolution, which shifts the rack by one pitch, also requires the rotation of the work by one pitch (rotation C). In such a case all mayor cutting forces are tangential to the hob and directly translate into the torque which is required to rotate the hob.
In case of helical gears, the hob axis is inclined to the work axis by the value of the helix angle with the possible addition or subtraction of the hob lead angle (depending on the lead direction). One hob revolution (in case of a single start hob) requires a shift of the virtual generating rack, N, in direction “G” by one pitch. If, for example, an external cylindrical work gear is positioned on the opposite side of the rack than the hob, and if this work gear is “engaged” with the virtual generating rack, then the hob will cut involute teeth onto the work gear blank while it rotates (direction F). The work gear has to rotate one pitch during each hob revolution (one start hob). Because the generating rack has to shift in direction “G” while the hob rotates, the work gear will also have to rotate in direction “C” in order generate the involute profile and also in order to work its way around the work gear and cut all the teeth (slots) on the work gear circumference.
FIG. 2 shows a three dimensional graphic of a shaper cutter and a virtual generating rack. While the shaper cutter rotates (as indicated by Sk) around its axis, the generating rack shifts in direction “G” and the involute profile of the shaper cutter teeth will form the trapezoidal reference profile of the rack. Although the described cutter rotation and rack shift will form the profile of the rack, it will not provide any cutting action. The shaper cutter teeth have the involute profile which is required to form the straight profile of the rack teeth in a radial plane (perpendicular to the axis of the shaper cutter). The stroke motion “V” in the axial direction of the shaper cutter is required to introduce a cutting action and is also necessary to cut the face width of a gear. If the length of the stroke is equal to the width of the rack, then it is possible to cut a cylindrical gear with the same face width as shown left in FIG. 2. While the generating rack shifts in direction “G” e.g. by one pitch, the work which is engaged with the rack has to rotate also by one pitch (rotation C). In the case, shown in FIG. 2, all major cutting forces are directed in axial shaper cutter direction.
Shaping is a method where a cylindrical pinion-shaped cutter strokes axially (V in FIG. 2) while it is engaged with an external or internal work piece. Every forward stroke removes material while, simultaneously to the stroking, a continuous index rotation between shaper cutter and work piece is performed. While the shaper cutter rotates one pitch (rotation Sk) the generating rack shifts one pitch in direction “G” and the work gear rotates one pitch in rotational direction “C” (in FIG. 2). Every reverse stroke is unproductive which makes shaping a rather slow process. Shaping has its strength in the machining of internal gears (which is not possible with hobbing) or gears which allow no over-travel clearance behind the end of the teeth to be machined (also often not possible with hobbing).
FIG. 3 shows the orientation of a Power skiving cutter and an internal gear, front and top view. While the cutter rotates the involute profiles of its teeth form the straight profiles of a virtual generating rack (not shown in FIG. 3). The rotation of the cutter shifts the generating rack sideways (like in FIG. 2). Covering the width of the generating rack teeth (equivalent with the face width of a cylindrical gear to be cut) requires a feed motion of the cutter in axial work gear direction (Y4, Z4).
In contrast to the shaper cutter in FIG. 2, the cutting action in power skiving is not generated by axial stroking but merely by the relative motion between skiving cutter and work gear (during the synchronized rotation of both) which is directed in lead direction of the work gear teeth. The relative motion is created with the inclination angle between work and cutter (see shaft angle Σ in FIG. 3). The cutting teeth are engaged in the slots of the work piece while cutter and work piece rotate and create the velocities Vtool and Vwork as shown in FIG. 3. The difference between the two peripheral velocities is utilized as cutting velocity Vcut. Thus, the cutting velocity Vcut is a function of the cutter RPM (or angular velocity ωtool) and the inclination angle Σ:Vcut=ωtool·sin Σ
With power skiving, the tool has a complicated geometry which is determined and manufactured for one specific work gear geometry. A solid high speed steel cutter 1 as shown in FIG. 4 is the most common type of tool utilized in the power skiving process. The cutter disk 1 is manufactured for example from high speed steel material. The cutter disk 1 has a plurality of cutting teeth (or blades) 2 which have a front face 3, two cutting edges 4 and 5, two side relief surfaces 6 and 7 behind the cutting edges 4 and 5 as well as a top relief surface 8.
Correction methods for pressure angle changes are known in the state of the art if such a tool produces teeth with a pressure angle error. Such correction methods include:                A. Re-grind the all the teeth (blades) 2 of cutter disk with a corrected pressure angle.        B. Three dimensional cutter inclinations which utilize a projection of the profile of the tool front face 3 in the cutting process instead of the real front face profile 3.        
Method A is expensive and time consuming. There may be several weeks of turn-around time required in order to re-shape and re-coat the blade profiles 4 and 5 of the cutter disk 1. In most cases, such a re-working is not even possible because the corrected profile would require altering the diameter and/or the thickness of the disk 1. A diameter change will cause additional tooth profile distortion of the manufactured work gear 15 and therefore is not permissible. Changing the thickness of the cutter disk 1 is in most cases not possible because the side relief behind the front face cutting profile (surfaces 6 and 7) reduces the thickness of the cutting teeth which will cause tooth thickness errors in the produced gears.
Method B can be applied within very small limits. Changing the three-dimensional orientation of the cutter disk (FIG. 3) might correct the pressure angle error but also will distort the involute profile which causes secondary profile errors in the produced work gears. The additional tool inclinations required for such a correction will also reduce or increase the technological blade angles such as side rake angle (surface 3), side relief angles (surfaces 6 and 7) and the top relief angle (surface 8) which might have an adverse effect to the tool life and the produced surface finish.